[Paper Review] Fermion-induced quantum critical points: type-II Landau-forbidden transitions

Zi-Xiang Li, Yi‐Fan Jiang+2 more|arXiv (Cornell University)|Dec 24, 2015

Graphene research and applications3 citations

TL;DR

This paper proposes fermion-induced quantum critical points (FIQCP), a new class of second-order quantum phase transitions in two-dimensional Dirac semimetals that evade the Landau criterion's first-order restriction due to gapless fermions. Using renormalization group analysis and sign-problem-free Majorana quantum Monte Carlo simulations, it demonstrates continuous transitions for SU(N) fermions on a honeycomb lattice (N=2 to 6), establishing FIQCP as type-II Landau-forbidden transitions with experimental relevance in graphene-like materials.

ABSTRACT

According to Landau criterion, phase transitions must be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group (RG) analysis we show that second-order quantum phase transitions can occur at such putatively first-order transitions in strongly-interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical are induced by gapless fermions, we call them fermion-induced quantum critical points (FIQCP), which are type-II Landau-forbidden transitions. We further introduce a sign-problem-free model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale Majorana quantum Monte Carlo simulations show convincing evidences of a continuous quantum phase transition for N=2, 3, 4, 5, and 6, consistent with the RG analysis. We also discuss possible experimental realizations of the FIQCP in graphene-like materials.

Motivation & Objective

• To identify and characterize a new class of quantum phase transitions that bypass the Landau criterion's first-order restriction.
• To investigate the role of gapless fermions in stabilizing continuous transitions in strongly correlated Dirac semimetals.
• To provide a sign-problem-free model of SU(N) fermions on a honeycomb lattice to study the transition between Dirac semimetals and Kekule valence bond solids.
• To establish numerical evidence for continuous quantum phase transitions across multiple N values (N=2 to 6) using large-scale Majorana quantum Monte Carlo simulations.

Proposed method

• Employing renormalization group (RG) analysis to examine the stability of the Landau-Ginzburg free energy with cubic terms, revealing how gapless fermions can stabilize second-order transitions.
• Constructing a sign-problem-free model of SU(N) fermions on the honeycomb lattice to describe the transition from Dirac semimetals to Kekule valence bond solids.
• Implementing large-scale Majorana quantum Monte Carlo simulations to numerically probe the nature of the quantum phase transition for N=2 to 6.
• Analyzing critical exponents and scaling behavior from Monte Carlo data to distinguish between first- and second-order transitions.
• Using symmetry analysis to identify the presence of cubic terms in the Landau-Ginzburg free energy, which classically imply first-order transitions.
• Comparing RG predictions with numerical results to validate the existence of fermion-induced quantum critical points (FIQCP).

Experimental results

Research questions

• RQ1 Can second-order quantum phase transitions occur at transitions that are classically forbidden by the Landau criterion due to cubic terms in the free energy?
• RQ2 How do gapless Dirac fermions influence the stability of quantum critical points in two-dimensional systems?
• RQ3 What is the nature of the transition between Dirac semimetals and Kekule valence bond solids in SU(N) fermion models on the honeycomb lattice?
• RQ4 Can continuous transitions be observed numerically in sign-problem-free models for multiple N values (N=2 to 6)?
• RQ5 What are the experimental signatures and realizations of fermion-induced quantum critical points in graphene-like materials?

Key findings

• The paper establishes the existence of fermion-induced quantum critical points (FIQCP), a new class of type-II Landau-forbidden transitions that are second-order despite cubic terms in the Landau-Ginzburg free energy.
• Renormalization group analysis confirms that gapless fermions can stabilize second-order transitions at classically first-order-candidate points.
• Large-scale Majorana quantum Monte Carlo simulations provide strong numerical evidence for continuous quantum phase transitions for SU(N) fermions with N=2, 3, 4, 5, and 6.
• The simulations show consistent critical behavior across all N values, supporting the universality of the FIQCP mechanism.
• The study identifies a sign-problem-free model of SU(N) fermions on the honeycomb lattice that enables reliable numerical investigation of the Dirac semimetal to Kekule valence bond solid transition.
• The results suggest possible experimental realizations of FIQCP in graphene-based heterostructures and related two-dimensional materials with strong electron correlations.